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In the geophysical joint inversion, the gradient and Bayesian Markov ChainMonte Carlo (MCMC) sampling-based methods are widely used owing to their fastconvergences or global optimality. However, these methods either require thecomputation of gradients and easily fall into local optimal solutions, or costmuch time to carry out the millions of forward calculations in a huge samplingspace. Different from these two methods, taking advantage of the recentlydeveloped unscented Kalman method in computational mathematics, we extend aniterative gradient-free Bayesian joint inversion framework, i.e., Multi-taskunscented Kalman inversion (MUKI). In this new framework, information fromvarious observations is incorporated, the model is iteratively updated in aderivative-free way, and a Gaussian approximation to the posterior distributionof the model parameters is obtained. We apply the MUKI to the joint inversionof receiver functions and surface wave dispersion, which is well-establishedand widely used to construct the crustal and upper mantle structure of theearth. Based on synthesized and real data, the tests demonstrate that MUKI canrecover the model more efficiently than the gradient-based method and theMarkov Chain Monte Carlo method, and it would be a promising approach toresolve the geophysical joint inversion problems.

Multi-task unscented Kalman inversion (MUKI): a derivative-free joint inversion framework and its application to joint inversion of geophysical data